Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825v |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
-28644544318359375 = -1 · 38 · 59 · 76 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- 4 2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,27537,7962156] |
[a1,a2,a3,a4,a6] |
Generators |
[9646:942755:1] |
Generators of the group modulo torsion |
j |
1256216039/15582375 |
j-invariant |
L |
3.8575593106515 |
L(r)(E,1)/r! |
Ω |
0.27590742629129 |
Real period |
R |
6.9906768415188 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997312 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13965r1 1425h1 |
Quadratic twists by: 5 -7 |